Question

The rectangle below has an area of 144x^4 square meters and a width of 12x meters. What is the length of the rectangle?

Answer 1

EXPLANATION

Rectangle:

Area = 144x^2 square meters

Width= 12x meters.

As we know, the area of a rectangle is given by the following formula:

AREA = 2*(Length + Width)

Replacing values in the equation:

$144x^4=2\cdot(\text{length}+12x)$

Applying distributive property:

$144x^4=2\text{length + 24x}$

Adding similar terms:

$144x^4-24x\text{ = 2length}$

Dividing both sides by 2:

$72x^4\text{ - 12x = length}$

Now, we need to solve this equation:

Applying exponent rule: a^(b+c) = a^b*a^c

x^4=x*x^3

=74x^3x-12

Rewriting 12 as 2*6

Rewriting 74 as 2*37

=2*37x^3x-2*6x

Factor out common term 2x:

=2x(37x^3-6)

Answer: Length is 2x(37x^3-6)